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Divided 56 into 2 parts such that three times the first part exceesed one third of the second by 48 the parts are?
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Divided 56 into 2 parts such that three times the first part exceesed ...
Understanding the Problem
To solve the problem, we need to divide the number 56 into two parts, which we can denote as x and y. The problem gives us two conditions to work with:
1. The sum of the two parts is 56.
2. Three times the first part exceeds one third of the second part by 48.
Setting Up the Equations
Let’s convert the problem into equations:
1. x + y = 56 (Equation 1)
2. 3x = (1/3)y + 48 (Equation 2)
Solving the Equations
1. From Equation 1, we can express y in terms of x:
- y = 56 - x
2. Substitute y in Equation 2:
- 3x = (1/3)(56 - x) + 48
3. Simplifying the equation:
- 3x = (56/3) - (1/3)x + 48
- Multiply the entire equation by 3 to eliminate the fraction:
- 9x = 56 - x + 144
- 9x + x = 200
- 10x = 200
- x = 20
4. Now, substitute x back into Equation 1 to find y:
- y = 56 - 20
- y = 36
Final Parts
The two parts into which 56 is divided are:
- First Part (x): 20
- Second Part (y): 36
Verification
To verify, check the conditions:
1. x + y = 20 + 36 = 56 ✔
2. 3x = 3(20) = 60; (1/3)y + 48 = (1/3)(36) + 48 = 12 + 48 = 60 ✔
Thus, the solution is accurate. The parts are 20 and 36.
To solve the problem, we need to divide the number 56 into two parts, which we can denote as x and y. The problem gives us two conditions to work with:
1. The sum of the two parts is 56.
2. Three times the first part exceeds one third of the second part by 48.
Setting Up the Equations
Let’s convert the problem into equations:
1. x + y = 56 (Equation 1)
2. 3x = (1/3)y + 48 (Equation 2)
Solving the Equations
1. From Equation 1, we can express y in terms of x:
- y = 56 - x
2. Substitute y in Equation 2:
- 3x = (1/3)(56 - x) + 48
3. Simplifying the equation:
- 3x = (56/3) - (1/3)x + 48
- Multiply the entire equation by 3 to eliminate the fraction:
- 9x = 56 - x + 144
- 9x + x = 200
- 10x = 200
- x = 20
4. Now, substitute x back into Equation 1 to find y:
- y = 56 - 20
- y = 36
Final Parts
The two parts into which 56 is divided are:
- First Part (x): 20
- Second Part (y): 36
Verification
To verify, check the conditions:
1. x + y = 20 + 36 = 56 ✔
2. 3x = 3(20) = 60; (1/3)y + 48 = (1/3)(36) + 48 = 12 + 48 = 60 ✔
Thus, the solution is accurate. The parts are 20 and 36.
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Divided 56 into 2 parts such that three times the first part exceesed one third of the second by 48 the parts are?
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Divided 56 into 2 parts such that three times the first part exceesed one third of the second by 48 the parts are? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Divided 56 into 2 parts such that three times the first part exceesed one third of the second by 48 the parts are? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Divided 56 into 2 parts such that three times the first part exceesed one third of the second by 48 the parts are?.
Divided 56 into 2 parts such that three times the first part exceesed one third of the second by 48 the parts are? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Divided 56 into 2 parts such that three times the first part exceesed one third of the second by 48 the parts are? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Divided 56 into 2 parts such that three times the first part exceesed one third of the second by 48 the parts are?.
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